Given function g(x) = |2x - 5|. Find:
(a) the image of -1,
(b) the value of k if g(3k + 1) = 3.

The image of -1 for the function g(x) = |2x - 5| is 7. The values of k that make g(3k + 1) equal to 3 are k = 1 and k = 0.
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Answered by Anonymous | 2025-07-04

To solve the problem involving the function g ( x ) = ∣2 x − 5∣ , we'll break it into two separate parts:
(a) Finding the image of − 1 :
The image of a number a under a function g ( x ) is the value of g ( a ) . Let's find g ( − 1 ) :
g ( − 1 ) = ∣2 ( − 1 ) − 5∣
Calculate inside the absolute value:
2 ( − 1 ) = − 2
Then subtract 5:
− 2 − 5 = − 7
The absolute value of − 7 is 7 . So,
g ( − 1 ) = 7
(b) Finding the value of k if g ( 3 k + 1 ) = 3 :
We start with:
g ( 3 k + 1 ) = ∣2 ( 3 k + 1 ) − 5∣ = 3
Simplify inside the absolute value:
2 ( 3 k + 1 ) = 6 k + 2
Subtract 5:
6 k + 2 − 5 = 6 k − 3
Thus, we have:
∣6 k − 3∣ = 3
The absolute value equation ∣6 k − 3∣ = 3 can be split into two separate equations:

6 k − 3 = 3

6 k − 3 = − 3


Let's solve each equation:

6 k − 3 = 3
Add 3 to both sides:
6 k = 6
Divide by 6:
k = 1

6 k − 3 = − 3
Add 3 to both sides:
6 k = 0
Divide by 6:
k = 0


So the values of k that satisfy the equation are k = 1 and k = 0 .

Answered by RyanHarmon181 | 2025-07-06