If f(x) = -7x + 7 and g(f(x)) = 2x + 1, then g(2) = ?

Answer 1

g(2) means that f(x) = 2 = -7x + 7. Solving for x we get x = 5/7

So g(2) = 2x + 1 = 2(5/7) + 1 = 17/7

Answer 2

This problem is sort of the "backwards" of the way these composition functions are usually presented, so to work it, we need to think it backwards.

Here is what we want: g(2)

That means that for g[f(x)] to be g(2), we need f(x) = 2.

f(x) = -7x+7 so we set that =2 and find that x = 5/7

Now start going forward again using x=5/7

f(5/7) = -7(5/7) + 7 = 2

So g[ f(5/7) ] = g(2)

Plugging in x=5/7 everywhere in g[ f(x) ] = 2x + 1, we get

g[ f(5/7) ] = 2(5/7) + 1

g(2) = 10/7 + 1

g(2) = 10/7 + 7/7

g(2) = 17/7