Question

Consider the following function. \[ f(x)=\left\{\begin{array}{ll} 3^{x} & \text { if } x \leq 1 \\ 4-x & \text { if } 15 \end{array}\right. \] Find the following values. \[ f(1)= \] \[ f(5)= \] \[ \li

Answer 1

Explanation:

Let's evaluate the function f(x)f(x) for the given values of xx:

f(1)f(1):

Since x=1x=1 falls into the first case where x≤1x≤1, we use the function f(x)=3xf(x)=3x:

f(1)=31=3f(1)=31=3

f(5)f(5):

Since x=5x=5 falls into the second case where x>1x>1, we use the function f(x)=4−xf(x)=4−x:

f(5)=4−5=−1f(5)=4−5=−1

f(15)f(15):

Since x=15x=15 falls into the second case where x>1x>1, we use the function f(x)=4−xf(x)=4−x:

f(15)=4−15=−11f(15)=4−15=−11

So, the values of the function f(x)f(x) for the given values of xx are:

f(1)=3f(1)=3

f(5)=−1f(5)=−1

f(15)=−11f(15)=−11