Provide a linear function such as f(1-x)=3x+2?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to express f(1-x) = 3x + 2 as a linear function. A linear function is one in which the highest power of x is 1.

f(1 - x) = 3x + 2

let 1 - x = y or x = 1 - y

f(1 - x) = 3x + 2

=> f(y) = 3(1 - y) + 2

=> f(y) = 3 - 3y + 2

=> f(y) = -3y + 5

This gives the required function as f(x) = -3x + 5

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll recall which is the standard form of a linear function;

f(x) = ax + b

To determine the linear function, we'll have to identify the coefficients a and b.

Since we know the result of f(1-x), we'll replace x by (1-x) in the standard form:

f(1-x) = a(1-x) + b

f(1-x) = a - ax + b (1)

But, from enunciation, we know that f(1-x) = 3x+2 (2)

We'll equate (1) and (2) and we'll get:

-ax + a + b = 3x + 2

Comparing, we'll get:

-a = 3 => a = -3

a + b = 2 <=> -3 + b = 2 => b = 5

The requested linear function is f(x) = -3x + 5.

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