Question

What is the inverse of the linear function t(x) = (5/2)x - 102? A) t⁻¹(x) = 4x + 4 B) t⁻¹(x) = (2/5)x + 10 C) t⁻¹(x) = ?x + 100 D) t⁻¹(x) = (-5/2)x + 10 E) None of the above are t⁻¹(x).

Answer 1

The inverse function of t(x) = (5/2)x - 102 is t⁻¹(x) = (2/5)x + 10.

Step-by-step explanation:

To find the inverse of the linear function t(x) = (5/2)x - 102, we must switch the roles of x and y and solve for y. This will give us the equation of the inverse function t⁻¹(x).

Let's start by replacing t(x) with y: y = (5/2)x - 102.

Next, we'll swap x and y: x = (5/2)y - 102.

Now let's solve for y:

x + 102 = (5/2)y.

Next, multiply both sides by the reciprocal of (5/2), which is 2/5:

(2/5)(x + 102) = y.

Therefore, the inverse function t⁻¹(x) is equal to (2/5)x + 10.

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