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Lunna [17]
3 years ago
12

Please help. I don't understand where to start with this one. If the slope of a strictly decreasing function at the point (a, b)

is –4, what is the slope of the inverse of the function at the point (b, a)?
a. -1/4
b. –4
c. –1
d. The slope cannot be determined without knowing the equation of the function.
Mathematics
2 answers:
Bingel [31]3 years ago
7 0

Answer:

a.-\frac{1}{4}

Step-by-step explanation:

We are given that

Slope of strictly decreasing function at the point (a,b) is -4.

We have to find the slope of the inverse of the function at the point (b,a).

Suppose , we have a function

y=f(x)=-4x+2

Slope of function f(x) at (x,y)=-4

-4x=y-2

x=-\frac{1}{4}(y-2)

Replace x by y and y by x.

y=-\frac{1}{4}(x-2)

Now, substitute y=f^{-1}(x)

g(x)=f^{-1}(x)=-\frac{1}{4}(x-2)

Differentiate w.r.t x

g'(x)=\frac{-1}{4}  Using rule (\frac{dx^n}{dx}=nx^{n-1})

Slope of inverse of function f(x) at (y,x)=-\frac{1}{4}

Hence, the slope of inverse of the function at the point (b,a)is -\frac{1}{4}.

Option a is true.

pashok25 [27]3 years ago
6 0
Just assume the equation is y=-4x
to find the inverse you switch x and y so your equation becomes x=-4y, and then solve for y and you get, y=(-1/4)x so the slope is A)-1/4
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