Answer to Question #300419 in Calculus for ezekiel

Question

if f(x)=x² and g(x)=2x-1.find1.gf(x) 2.fg(x) 3.inverse of g(x)?

Answer 1

1.

$$(g\circ f)(x)=2x^2-1$$

2.

$$(f\circ g)(x)=(2x-1)^2$$

3.

$$g(x)=2x-1$$

Replace $g(x)$ with $y$

$$y=2x-1$$

Replace $y$ with $x$

$$x=2y-1$$

Solve for $y$

$$y=\dfrac{1}{2}x+\dfrac{1}{2}$$

Replace $y$ with $g^{-1}(x)$

$$g^{-1}(x)=\dfrac{1}{2}x+\dfrac{1}{2}$$