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topjm
2 months ago
10

If f(x)=5x-25 and g(x) = 1/5x+5 which expression could be used to verify g(×) is the inverse of f(×)

Mathematics
2 answers:
zzz [12.3K]2 months ago
8 0

Answer:

Therefore, g(x) is the inverse function of f(x).

Step-by-step explanation:

The functions provided are f(x) = 5x − 25 and g(x)=\frac{1}{5}x+5

To verify that g(x) is the inverse of f(x), we substitute g(x) into f(x):

(f ∘ g)(x) = f(g(x))

              = 5(\frac{1}{5}x+5)-25

             = x + 25 − 25

             = x

Next, substitute f(x) into g(x):

(g ∘ f)(x) = g(f(x))

              = \frac{1}{5}x+5

              = \frac{1}{5}(5x-25)+5

              = x − 5 + 5

              = x

In both compositions, the output simplifies to x

This confirms both functions are inverses of each other.

Thus, g(x) is the inverse of f(x).

AnnZ [12.3K]2 months ago
4 0

Answer:

The expression usable to check whether g(x) is the inverse of f(x) is option b: 1/5(5x - 25) + 5.

Detailed explanation:


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