Consider these functions: f(x)= -2x - 1 g(x)= -1/2x + 1/2 Which statements, if any, are true about these functions? I. The function f(g(x)) = x for all real x. II. The function g(f(x)) = x for all real x. III. Functions f and g are inverse functions. A. I only B. II only C. I, II, and III D. None of the statements are true.

The correct option is: A. I only

We have functions:

Now, replace x in h(x) by

So,

Now, g(h(x))

g(h(x)) = g(-2x-1)

Since

As g(h(x)) ≠ h(g(x)),

Therefore, both functions are not inverses of each other.

Hence A. I only

The function h(g(x)) = x is the only correct option.

So, option A is correct.

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A. I only

Step-by-step explanation:

Given the functions

h(x)= -2x - 1 g(x)= -1/2x + 1/2

h(g(x) =h( -1/2x + 1/2)

=f((-x+1)/2)

We are to replace x in h(x) with -x+1/2

h((-x+1)/2) = -2(-x+1)/2 + 1

h((-x+1)/2) = -(-x+1)+1

h((-x+1)/2)= x-1+1

h((-x+1)/2) = x

h(g(x) = x

Also for g(h(x))

g(h(x)) = g(-2x-1)

Since g(x) = -x+1/2

g(-2x-1) = -(-2x-1)+1/2

g(-2x-1) =2x+1+1/2

g(-2x-1) = 2x+2/2

g(-2x-1) = 2(x+1)/2

g(-2x-1) = x+1

Sine g(h(x)) ≠ h(g(x)), hence both functions are not inverses of each other

Hence I. The function h(g(x)) = x is the only correct option. Option A is correct

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step-by-step explanation:

your answer is the frist one

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