Question

QF Q6.) Find the following function for c.

Answer 1

$\text{Solution for}$ $f(x)=2x-2$ and $g(x)=5x^2-3$

$\dfrac{d}{dx} \left(2x-2\right)=2 \ \ \ =\ \textgreater \ \ \ \ \dfrac{d}{dx}\left(2x\right)-\dfrac{d}{dx}\left(2\right)$ 

$2\dfrac{d}{dx}\left(x\right) = 2$ 

$\dfrac{d}{dx}\left(2\right) = 0$ 

$\text{Therefore, 2 - 0 = 2}$

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$\dfrac{d}{dx}\left(5x^2\right)-\dfrac{d}{dx}\left(3\right)$ 

$5\dfrac{d}{dx}\left(x^2\right) =\ \textgreater \ 5 * \:2x =\ \textgreater \ 10x$ 

$5*2^2 -3$ 

$g(f(2)) = 17$ 

$2*17 -2 = 32$ 

Answer 2

(f∘g)(x) = f(g(x))
(f∘g)(2) = f(g(2)) = f(5·2² -3) = f(17) = 2·17 -2 = 32

(f∘g)(2) = 32