Question

QF Q6.) Find the following function for c.

Answer 1

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


`(d)/(dx) \left(2x-2\right)=2 \ \ \ =\ \textgreater \ \ \ \ (d)/(dx)\left(2x\right)-(d)/(dx)\left(2\right)`


`2(d)/(dx)\left(x\right) = 2`


`(d)/(dx)\left(2\right) = 0`


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

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`(d)/(dx)\left(5x^2\right)-(d)/(dx)\left(3\right)`


`5(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