Given the function f(x) = -5|x + 1| + 3, for what values of x is f(x) = -12?

Solution:

f(x) = -5|x + 1| + 3

Here f(x) = -12

Substitute f(x) and solve for x

- 12 = -5|x + 1| + 3

By subtracting 3 on both sides

- 12 - 3 = -5|x + 1| + 3 - 3

- 15 = -5|x + 1|

By dividing -5 on both sides

3 = |x + 1|

We get absolute values for the function.

x + 1 = 3 and x + 1 = -3

By subtracting 1 on both sides

x + 1 - 1 = 3 - 1 and x + 1 - 1 = - 3 - 1

x = 2 and x = - 4

Therefore, the values of x are 2 and - 4.

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Given the function f(x) = -5|x + 1| + 3, for what values of x is f(x) = -12?

Summary:

Given the function f(x) = -5|x + 1| + 3, the values of x are 2 and - 4 when f (x) = -12.