Question

PLS HELP Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x)).
x –6 –4 –1 1 5
g(x) 16 10 1 –5 –17
h(x) –11 –7 –1 3 11
A. -5
B. -5/6
C. 5/6
D. 5

Answer 1

Using linear and composite functions, it is found that the x-intercept of g(h(x)) is $x = -\frac{5}{6}$, given by option B.

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The equation of a line is:

$y = mx + b$

In which:

• m is the slope.
• b is the y-intercept.

Function g:

• Two of the points are (-6,16) and (-4,10).
• The slope is given by change in y divided by change in x, thus:

$m = \frac{10 - 16}{-4 - (-6)} = -3$

Thus:

$g(x) = -3x + b$

Point (-4,10) means that when $x = -4, g(x) = 10$, and we use this to find b, so:

$10 = -3(-4) + b$

$12 + b = 10$

$b = -2$

Then

$g(x) = -3x - 2$

Function h:

• Two of the points are (-6,-11) and (-4,-7).
• The slope is:

$m = \frac{-7 - (-11)}{-4 - (-6)} = \frac{4}{2} = 2$

Thus:

$h(x) = 2x + b$

Point (-4,-7) means that when $x = -4, h(x) = -7$, and we use this to find b, so:

$-7 = 2(-4) + b$

$-8 + b = -7$

$b = 1$

Then

$h(x) = 2x + 1$

The composite function is:

$g(h(x)) = g(2x + 1) = -3(2x + 1) - 2 = -6x - 3 - 2 = -6x - 5$

The x-intercept it the zero of the function, thus:

$-6x - 5 = 0$

$6x = -5$

$x = -\frac{5}{6}$

Which is option B.

A similar problem is given at brainly.com/question/21010520

Answer 2

Answer:

-5/6

Step-by-step explanation: