Given f(x) = x² and g(x) = 5x + 3 Evaluate i) gf(-2) ii) g¯¹(x) ...

i) gf(-2)

Given two function
g(x) and f(x), the function gf(x) = g[f(x)]

it is
given:

g(x) = 5x + 3, and f(x) =
x^2

Therefore:

gf(x) = g[f(x)]
= g(x^2) = 5(x^2) + 3

= 5x^2 +
3

And

gf(-2) = 5(-2)^2 + 3  =
5*4 +3 = 20 + 3 = 23

ii)
g¯¹(x)

When gx has the form y =
g(x),

g inverse(x) represents the same function in the
form;

x = a function of y

We
convert g(x) in the g (inverse(x) form as follows:

y = 5x
+3

5x = y - 3

x = y/5 -
3/5

Interchanging x and y, the function g inverse(x)
becomes

g inverse(x) --> y = x/5 -
3/5