# Given the function f(x)=2x-3, find the function g(x)=f(x+1)+f(x-1)?

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The function f(x) = 2x - 3

f(x + 1) = 2(x + 1) - 3

=> 2x + 2 -3

=> 2x - 1

f(x - 1) = 2(x - 1) - 3

=> 2x - 2 - 3

=> 2x - 5

g(x) = f(x + 1) + f(x - 1)

=> 2x -1 + 2x - 5

=> 4x - 6

**The required function g(x) = 4x - 6**

Since f(x) is a linear function, then f(x+1) and f(x-1) will be also linear functions.

Since g(x) is the result of adding two linear functions, then g(x) is a linear function, too.

f(x+1) = 2x + 2 - 3

f(x+1) = 2x - 1 (1)

f(x-1) = 2x - 2 - 3

f(x-1) = 2x - 5 (2)

We'll add (1) and (2):

g(x) = 2x - 1 + 2x - 5

g(x) = 4x - 6

**The requested function g(x) is: g(x) = 4x - 6.**

f(x+1) = 2x + 2 - 3 (since the function is 2x -3 )

f(x+1) = 2x - 1 x 1

f(x-1) = 2x - 2 - 3

f(x-1) = 2x - 5 x2

(1)+(2)

g(x) = 2x - 1 + 2x - 5

**g(x) = 4x - 6**

we are dealing with functions, linear functions to be specific, so you need to know that f(x) = f(x+1) according to the q.

so we'll go like this;

f(x+1) = 2x + 2 - 3 (since the function is 2x -3 )

f(x+1) = 2x - 1 x 1

f(x-1) = 2x - 2 - 3

f(x-1) = 2x - 5 x2

so we're gonna add up funtion (1) & (2)

g(x) = 2x - 1 + 2x - 5 (which give the following below)

g(x) = **4x - 6**