Question

Given the function f(x) = 4|x – 5| + 3, for what values of x is f(x) = 15? x = 2, x = 8 x = 1.5, x = 8 x = 2, x = 7.5 x = 0.5, x = 7.5

Answer 1

`f(x)=4|x-5|+3\\\\f(x)=15\\\Downarrow\\4|x-5|+3=15\qquad\text{subtract 3 from both sides}\\\\4|x-5|=12\qquad\text{divide both sides by4}\\\\|x-5|=3\iff x-5=-3\ \vee\ x-5=3\qquad\text{add 5 to both sides}\\\\\boxed{x=2\ \vee\ x=8}`

Answer 2

x = 2 , x = 8

Explanation:

The absolute value function is given by

`f(x)=4|x-5|+3`

Substitute f(x)=15

`4|x-5|+3=15`

Subtract 3 to both sides

`4|x-5|=12`

Divide both sides by 4

`|x-5|=3`

Eliminate the absolute sign

`x-5=-3,x-5=3`

Solve for x

`x=2,x=8`

Therefore, for x = 2 and x = 8, f(x) = 15