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marusya05 [52]
4 years ago
15

Suppose a function f has an inverse. If f(2)=6 and f(3)=7, find: f−1(6)

Mathematics
2 answers:
myrzilka [38]4 years ago
5 0

Answer:

f^{-1}(6) = 2

Step-by-step explanation:

Given

f(2) = 6

f(3) = 7

Required

f^{-1}(6)

First, we need to determine the slope of the function using;

m = \frac{y_1 - y_2}{x_1 - x_2}

From the given parameters;

In f(2) = 6

x = 2; y =6 --- Take this as x1 and y1

In f(3) = 7

x = 3; y = 7 --- Take this as x2 and y2

m = \frac{y_1 - y_2}{x_1 - x_2} becomes

m = \frac{6 - 7}{2 - 3}

m = \frac{- 1}{ - 1}

m = 1

Next, we determine the equation of the function using

y - y_1 = m(x - x_1)

Substitute the values of x1,y1 and m

y - 6 = 1(x - 2)

Open bracket

y - 6 = x - 2

Add 6 to both sides

y - 6 + 6 = x -2 +6

y = x + 4

Next is to determine the inverse function by swapping the positions of x and y

x = y + 4

Make y the subject of formula;

y = x - 4

Replace y with f^{-1}(x)

f^{-1}(x) = x - 4

Now, we can solve for f^{-1}(6)

Substitute 6 for x

f^{-1}(6) = 6 - 4

f^{-1}(6) = 2

ipn [44]4 years ago
3 0
I GOT THAT THANG ON MY HOMIEEEEE
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