Consider the following function: f(x) = a/(x-1) +1. If the graph of the function passes through the point, (2, 5), what is the value of 'a'?

Question

BlackTom AI · Accepted Answer

To solve, start from the given point on the graph: when x = 2, f(x) = 5.
Next, substitute x = 2 into the function f(x) = a/(x-1) + 1: f(2) = a/(2-1) + 1 = a/1 + 1 = a + 1.
Set this equal to the given y-value: a + 1 = 5.
Now solve for a: subtract 1 from both sides to get a = 4.

Option a. 1: If a = 1, then f(2) = 1 + 1 = 2, which does not equal 5, so this is incorrect.
Option b. -4: If a = -4, then f(2) = -4 + 1 = -3, which is not 5, so this is incorrect.
Option c. 4: If a = 4, then f(2) = 4 + 1 = 5, which matches the given point, so this is correct.
Option d. 2: If a = 2, then f(2) = 2 + 1 = 3, which is not 5, so this is incorrect.

MUF0091 Mathematics Unit 1 - Semester 1, 2025 3.6 Power functions review questions

Consider the following function: f(x) = a/(x-1) +1. If the graph of the function passes through the point, (2, 5), what is the value of 'a'?

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