Question

Given the piecewise function shown below, select all of the statments that are true.

f(x)= { 2x,x<1}
5, x=1
X^2, x>1
Everything is in the brackets

A. f(5)=1
B. f(2)=4
C. f(-2)=4
D. f(1)=5

Answer 1

The given the piecewise function is :


`f(x) = \[ \begin{cases} 2x & x \ \textless \ 1 \\ 5 & x=1 \\ x^2 & x\ \textgreater \ 1 \end{cases} \]`

To find f(5) ⇒ substitute with x = 5 in the function → x²
∴ f(5) = 5² = 25


To find f(2) ⇒ substitute with x = 5 in the function → x²
∴ f(2) = 2² = 4

To find f(-2) ⇒ substitute with x = 5 in the function → 2x
∴ f(-2) = 2 * (-2) = -4

To find f(1) ⇒ substitute with x = 1 in the function → 5
∴ f(1) = 5
================================
So, the statements which are true:

`\framebox {B. f(2) = 4} \ \framebox {D. f(1) = 5}`