Question

If f(x) = x² + 5 and g(x) = 3x, find (f o g)(x) and (g o f)(x) .

Answer 1

`(f \circ g)(x) = 9x^2 + 5\\\\\\(g \circ f)(x) = 3x^2 + 15`

Explanation:

We are given

`f(x) = x^2+5\\\\g(x) = 3x\\\\(f\circ g)(x) = f(g(x))\\\\`

To find this, wherever you see an x in f(x) substitute the expression in g(x)

`(f\circ g)(x) = f(g(x))\\\\= f(3x)\\\\= (3x)^2 + 5\\\\=9x^2 + 5\\\\\\`

To find
`(g \circ f)(x) = g(f(x))\\\\`

Wherever there is an x in the expression for g(x) substitute that x with the expression in f(x)

`(g \circ f)(x) = g(f(x))\\\\\\= g(x^2 + 5) = 3(x^2 + 5) \\\\= 3x^2 + 15`