A decreasing function g satisfies g(4) = 6 and g'(4) = -2. Which of the following statements about the inverse of g must be true? a. (g^-1)'(6) = -2
b. (g^-1)'(-2) = 4
c. (g^-1)'(6) = -2
d. (g^-1)'(6) = -1/2

The statement that is true about the inverse of g from the given options is;

Option D; (g ⁻¹)'(6) = -1/2

The theorem for inverse functions is one that is stated by the relationship that if f(x) = y, then the derivative of the inverse function is given as;

(f ⁻¹)'(y) = 1/f'(x) = 1/f'(f ⁻¹(y))

From the question, we see that; g(4) = 6 and g'(4) = -2. Thus, from the theorem, we can see that;

(g ⁻¹)'(6) = 1/g'(4)

Plugging in -2 for g'(4) gives;

(g ⁻¹)'(6) = -1/2

Looking at the options, the only one that corresponds with our answer is Option D.

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The inverse function theorem (terms and conditions apply) says that, if f(a) = b, then

(f ⁻¹)'(b) = 1 / f '(a) = 1 / f '(f ⁻¹(b))

We're given that g (4) = 6, so from the theorem it follows that

(g ⁻¹)'(6) = 1 / g '(4) = -1/2

so only D must be true.

B might also be true, but we don't have enough information to determine that.

the least common denominatore of 7 and 2 is 9

step-by-step explanation:

7+2=9

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is