Let f(x)=5x and g(x)=x^2+1, when the domain of x is all real numbers.

Question

1. Let f(x)=5x and g(x)=x^2+1, when the domain of x is all real numbers.
a. Find f^-1(x).
b. Find (f ° g)(7).

Answer 1

Hi Megan,

 

a) To find the inverse of a function, solve for x and then switch x and y. Here is how:

 

f(x) = 5x, which is the same as y = 5x

x = y/5

now switch x and y

y = x/5, which is the inverse f^-1(x)

f^-1(x) = x/5

 

b) Second part is asking you the composite function of f(x) and g(x).

(f o g)(x) = f(g(x))  Basically, we plugged in g(x) for x in f(x).

= 5(x^2 + 1)

= 5x^2 + 5

Then,

(f o g)(7) = 5*7^2 + 5

= 250