Question

Suppose f left parenthesis x right parenthesis equals 1 minus x squared and g left parenthesis x right parenthesis equals 2 x plus 5. Find the value of f(g(-1).

Answer 1

f(g(-1)) = -8

Explanation:

⭐ The two equations we are given are:

• 
  `f(x) = 1-x^2`
• 
  `g(x) = 2x + 5`

This problem is an example of composite functions.

⭐What are composite functions?

• Composite functions are functions inside of a function
• You compute the value of an x-value for one function, and use that value for another function.

First, we have to compute the value for the 2nd function you see. The 2nd function is inside f(x), and it is g(-1).

Essentially, we have to find the corresponding y-value for when x = -1 in g(x)

`g(-1) = 2(-1) + 5`

`g(-1) = 3`

Next, take this value and substitute it as the x-value for f(x).

`f(3) = 1-x^2`

Now we have to find the y-value for f(x) for when x = 3.

`f(3) = 1 -3^2`

⚠️⚠️⚠️!!! CAUTION !!! ⚠️⚠️⚠️

Some people may make the mistake of computing f(3) like this:

`f(3) = 1 - 3^2`

`f(3) = 1+9\\f(3) = 10`

This is wrong because only 3 is being squared, not -3. Make sure to read the equations you are given carefully to avoid mistakes like this.

`f(3) = 1-3^2\\f(3) = 1-9\\f(3) = -8`

∴ f(g(-1)) = -8