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

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.