Question

What is the value of f(-4)?

f(x) = {-10 if x < - 5
{x (to the third power) if -5 <_ x<_ 2
{2x + 4 if x > 2

A. -64
B. -12
C. -10
D. -4

Answer 1

Given is a piecewise function which follows different expressions according the the value of input x.

Given
`f(x)=\left \{ {{-10, \;if \;x<5} \atop {x^3, \;if \;-5}\leq x \leq 2} \atop {2x+4, \;if\;x>2} } \right.`

It says to find f(-4) i.e. the value of function f(x) at x = -4.

At point x = -4, f(x) is x³, if -5 ≤ x ≤ 2.

So, f(-4) = (-4)³

f(-4) = -4 × -4 × -4

f(-4) = -64.

Hence, option A is correct i.e. -64.