Solution for F(x)= x^24 f(2)f(h)Eq1) or equivalently if the following equation holds for all such x f (x) − f (− x) = 0 {\displaystyle f(x)f(x)=0} Geometrically, the graph of an even function is symmetric with respect to the y axis, meaning that its graph remains unchanged after reflection about the y axis Examples of even functions are The absolute value x ↦ x , {\displaystyle x\mapsto x,} x ↦ x 2Δ = b 24ac Δ = 4 24·1·(1) Δ = The delta value is higher than zero, so the equation has two solutions We use following formulas to calculate our solutions
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If f(x)=4^x/4^x 2 then f(1/1997)
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We have a function given in this problem If we want, we can evaluate this function at a specific value for x The notation given, f(1), tells us𝑓(𝑥)=(4𝑥 − 3)6𝑥 − 4 𝑓(𝑓𝑥) = 4𝑓(𝑥) − 36𝑓(𝑥) − 4 𝑓𝑜𝑓𝑥 = 44𝑥 − 36𝑥 − 4 − 364𝑥 − 36𝑥 − 4Put x = y = z = 1 = 4*3 3A If = 4 (xyz) then find A = ?
Skill 1 Evaluating Functions Evaluating functions involves putting numbers into the function to get the result Example A function is given by f(x) = 3x1, Find f(10) All this requires is to replace x with 10 and calculate the result When we input 10 into this function that would look like f(\textcolor{red}{10}) = 3\times \textcolor{red}{10} 1 = 31If f (x) = x1/x1 then find the value of f (2x) Find the answer to this question along with unlimited Maths questions and prepare better for JEE examinationF(x1)=3x4 Which can be written as f(X1)=3(x1) 7 Hence, f(x)=3x 7 Therefore f(4)= 3*(4) 7 f(4)=12–7 f(4)=19
The Lagrange interpolation formula is a way to find a polynomial which takes on certain values at arbitrary points Specifically, it gives a constructive proof of the theorem below This theorem can be viewed as a generalization of the wellknown fact that two points uniquely determine a straight line, three points uniquely determine the graph of a quadratic polynomial, four points uniquelySal finds the inverses of f(x)=x4 and g(x)=2x1 Sal finds the inverses of f(x)=x4 and g(x)=2x1 opposite we solve for X in terms of Y so let's subtract 4 from both sides you get Y minus 4 is equal to negative x and then to solve for x we could multiply both sides of this equation times negative 1 and so you get negative y plus 4 isSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
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Explanation Using the defined function, f(a) will produce the same result when substituted for x f(a) = a 2 – 5 Setting this equal to 4, you can solve for a a 2 – 5 = 4 a 2 = 9 a = –3 or 3F (x) = 4x24x f (4−x) = (4x2)2 f (x)f (1−x) = 1f ( )f ( ) = 1,f ( )f ( ) = 1⇒ sum = = 998 and so onDetermine composite and inverse functions for trigonometric, logarithmic, exponential or algebraic functions as part of Bitesize Higher Maths
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Integrate x/(x1) integrate x sin(x^2) integrate x sqrt(1sqrt(x)) integrate x/(x1)^3 from 0 to infinity;The inverse function of y=4/(x1) can be found by changing x to y and y to x, then solve for y So x=4/(2y1) Crossmultiply to get x(2y1)=4 Divide both sides by x to get 2y1=4/xWhen f(x)=x^42x^33x^2axb is divided by x1 andx1,we get remainders 19 and 5 respectivelyfind the remainder when f(x)is divided by x3 Get the answer to this question by visiting BYJU S Q&A Forum
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Graph f(x)=(1/4)x Rewrite the function as an equation Use the slopeintercept form to find the slope and yintercept Tap for more steps The slopeintercept form is , where is the slope and is the yintercept Find the values of and using the form The slope of the line is the value of , and the yintercept is the value of 102 A marathon is 262 miles long There is a water station every 1 1/4 miles along the race route How many water stations are needed for this marathIf f (x) = 4^x/4^x 2, f (x) f (1 x) = a and f (1/97) f (2/97) f (96/97) = b then order pair (a,b) is
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This example uses the basic function \(y = f(x)\) This can then be uses to draw related functions Notice that the main points on this graph are \(x = 2,\,1,\,4\) Graph of y = f(x) kIf f(x) is a product of several factors, any constants (terms in the product that do not depend on x) can be omitted For example, let f(x) = 6x 4 − 2x 3 5, and suppose we wish to simplify this function, using O notation, to describe its growth rate as x approaches infinity This function is the sum of three terms 6x 4, −2x 3, and 5F(x) f(1x) = 4 x /(4 x 2) 4 1x /(4 1x 2) = 4 x /(4 x 2) 2/(4 x 2) = 1 So f(1/97)f(96/97) = f(1/97) f(11/97) = 1 Similarly f(2/97)f(95/97) = 1 So the required sum = times Henct the required sum = 48
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1 Example 1 f(x) = x We'll find the derivative of the function f(x) = x1 To do this we will use the formula f (x) = lim f(x 0 0) Δx→0 Δx Graphically, we will be finding the slope of the tangent line at at an arbitrary point (x 0, 1 x 1 0) on the graph of y = x (The graph of y = x 1 is a hyperbola in the same way that the graph of Transcript Misc 2 If f(x) = x2, find (𝑓(11) − 𝑓(1))/((11 − 1 ) ) Let us first find f(11) and f(1) For f(11) f(11) = (11)2 = 11 × 11For example, we can multiply the functions f(x) = 1/ x and g(x) = 2 as, The domain of the ( f g )( x ) consists of all x values that are in the domain of both f and g In this example, f has domain { x x ≠ 0}, and g has domain all real numbers, therefore ( f g )( x ) has domain { x x ≠ 0}, because these values of x are in the domain of both f and g
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1 2 f00(ξ)(x 1 −x 0) Here, we simplify the notation and assume that ξ ∈ (x 0,x 1) If we now let x 1 = x 0 h, then f0(x 0) = f(x 0 h)−f(x 0) h − h 2 f00(ξ), which is the (firstorder) forward differencing approximation of f0(x 0), (53) Example 52 We repeat the previous example in the case n = 2 and k = 0 This time Q 2(x) = fIntegrate x^2 sin y dx dy, x=0 to 1, y=0 to pi;Formula of polynomials If the polynomial k 2 x 3 − kx 2 3kx k is exactly divisible by (x3) then the positive value of k is ____
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Answer and Explanation Become a Studycom member to unlock this answer!If f(x)=(x4/2√x), then f'(1) is (A) (5/4) (B) (4/5) 1 (D) 0 Check Answer and Solution for above question from Mathematics in Limits and Deriva f^(1)(x) = sqrt(x4) We have f(x) = x^24 And we seek the inverse function, f^(1)(x) My preferred approach is to put y = x^24 A And rearrange to form an explicit relationship x=f(y), and this function is the inverse, f^(1)(x) So, from A we have x^2 = y4 x = sqrt(y4) Thus f^(1)(x) = sqrt(x4) Note that by the formal definition f^(1)(x) is not a
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