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Prove that f(x) the inverse function of g(x) where f(x)= - 3x–6 and g(x)= - x/3–2

f ( x ) and g ( x ) are inverse functions when the following equations are true: f ( g ( x ))= x g ( f ( x ))= x To find ( f(g )( x) ) or ( g(f ( x )), use the inner function as the input for the outer funct...
SK
Answered by Sheela K. • Maths tutor
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Consider the function F(x)=17(x^4)+13(x^3)+12(x^2)+7x+2. A) differentiate F(x) B)What is the gradient at the point (2,440)

A point of notation: '#' is the beginning of a comment, we will use comments to note down thoughts and tricks at each stage of the problem A) let f(x) denote the differential of F(x) F(x)=17(x^4)+13(x^3)+12(...
DW
Answered by Dylan W. • Maths tutor
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Find the stationary points of the equation. f(x)=3x^2+4x.

Stationary points are points on the graph where the gradient is equal to 0.The gradient for any given point can be calculated by differentiating the original equation.f(x)=3x^2+4xDifferentiating gives:=> ...
EW
Answered by Ethan W. • Maths tutor
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i) differentiate xcos2x with respect to x ii) integrate xcos2x with respect to x

i) For this question we need to use the product rule as there are two functions that are being multiplied together Product Rule: (uv)'=u'v + v'u Apply this formula to the problem: xcos2x => u=x, u'=1 =&gt...
CP
Answered by Carina P. • Maths tutor
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How do we know the derivative of x^n

What does derivative mean? The derivative of a function the represents the gradient of the function for each value of x. Remark that the gradient of a function at point (x,f(x)) is equal to the gradient of a...
TP
Answered by Thomas P. • Maths tutor
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