Question

Evaluate the piecewise function below for f(1):

f(x) = { x^2 - 5 if x <= -1
3 - x^2 if -1 < x < 1
2x^2 + 3 if x >= 1 }

Write your answer as a single number.

Answer 1

We need to find f(1)

f(1) means x=1

Now we look at the three inequalities and choose the one where x=1 satisfies

x<=-1 , -1<x<1 and x>=1

x=1 satisfies the inequality x>=1

so we use the third function to find f(1)

`f(x) = 2x^2 + 3`

We plug in 1 for x and find f(1)

`f(1) = 2(1)^2 + 3`= 2 + 3 = 5

f(1) = 5