For f(x) = 4x+1 and g(x) = x^(2) -5 find (f ° g)(4)

Question

For
`f(x) = 4x+1` and
`g(x) = x^(2) -5` find
`(f` °
`g)`
`(4)`

Answer 1

`\bf \begin{cases} f(x)=4x+1\\ g(x)=x^2-5\\[-0.5em] \hrulefill\\ (f\circ g)(4)=f(~~g(4)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ g(4)=(4)^2-5\implies g(4)=16-5\implies \boxed{g(4)=11} \\\\\\ f(~~g(4)~~)\implies f(11)\implies f(11)=4(11)+1\implies \blacktriangleright f(11)=45\blacktriangleleft`

Answer 2

(f ° g)(4) = 45

Explanation:

f(x) = 4x+1 and g(x) = x^{2} -5 find (f ° g)(4)

"( f o g)(x)" means " f (g(x))"

That is, you plug something in for x, then you plug that value into g, simplify, and then plug the result into f.

f(g(x)) put x = 4 in g(x) = x² - 5

g(4) = 4² - 5 = 16 - 5 = 11

now put this g(x) = 11 where x = 4 in f(g(x)) = 4x + 1

f(g(4)) = f(11) = 4(11) + 1 = 44+1 = 45