Given f(x)=2x-7 find f^-1(1) .

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

It is given that f(x)=2x-7. We have to determine the inverse of f(x).

Let f(x) = 2x - 7 = y.

Express x in terms of y

y = 2x - 7

=> x = (y + 7)/2

interchange z x and y

=> y = (x + 7)/2

The inverse function f^-1(x) = (x + 7)/2

At x = 1, f^-1(1) = (1 + 7)/2 = 4

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we need to determine the expression of the inverse function, then we'll determine it's value.

We'll put f(x) = y

y = 2x - 7

Now, we'll move 2x to the left and y to the right:

-2x = -y - 7

We'll divide both sides by -2 to isolate x:

x = y/2 + 7/2

The expression of the inverse function is f^-1(x) = x/2 + 7/2

Now, we'll calculate f^-1(1):

f^-1(1) = 1/2 + 7/2

f^-1(1) = 8/2

f^-1(1) = 4

Therefore, the value of the inverse function f^-1(x), at x = 1, is f^-1(1) = 4.

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