Question

Find f(x) if it is known that f(x−2)=2x−4

Answer 1

Answer:

f(x) = 2x

Step-by-step explanation:

Remark

What I'm about to do is probably not the best way to do this question, but it is right. The plan is to take out a common factor on the right of f(x - 2) and then derive f(x) from that.

Solution

• f(x - 2) = 2x - 4              Take out a common factor on the right of f(x -2)
• f(x - 2) = 2(x - 2)             Now what that means is that in the original equation, wherever you saw an x, you put in x - 2. So the original equation must have been

Check

• f(x) = 2x                         To check this put x - 2 back in
• f(x - 2) = 2(x -2)              Remove the brackets.  
• f(x - 2) = 2x - 4  which is what it should be.

Answer 2

Answer:

f(x) = 2x

Step-by-step explanation:

Substitute y+2 for x

f(x−2)=2x−4

f(y+2-2)=2(y+2)-4

f(y)=2y+4-4

f(y)=2y

Substitute x for y

f(x)=2x