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
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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
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.
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