Posted by **Alyn** on Monday, February 9, 2009 at 9:12pm.

I was assigned this problem and I'm coming up against a brick wall. Here it is: Given that f(x) = 2x+1 and h(x) = 2x^2+4x+1, find a function g such that f(g(x)) = h(x)

I tried to factor 2x^2+4x+1 but ended up with something that didn't work. Am I missing something here? I'm so lost.

Thanks in advance,

Alyn

- calculus - functions! -
**Reiny**, Monday, February 9, 2009 at 9:33pm
since the resulting h(x) is quadratic, g(x) must have been quadratic

let g(x) = ax^2 + bx + c

then

f(g(x)) = 2(ax^2 + bx + c) + 1

= 2ax^2 + 2bx + 2c+1

but this is equal to 2x^2 + 4x + 1

so 2a = 2 , a = 1

2b = 4, b = 2

2c+1 = 1, c = 0

so g(x) = x^2 + 2x

## Answer this Question

## Related Questions

- calculus - A landscape architect wishes to enclose a rectangular garden on one ...
- calculus - A brick becomes dislodged from the top of a state building (at a ...
- Calculus - Find the sum and difference functions f + g and f – g for the ...
- Math - a wall in front of a house is shown below if 3/5 of the wall is brick how...
- Calculus - Find a function g such that g 0 (x) = sin(ln x 3 ( 4x . How many such...
- Calculus - Sketch the region enclosed by the given curves.? Decide whether to ...
- Math (Grade 12) - I need help with this problem (composite functions): If f(x...
- Calculus - I finished this problem but I wanted some feedback because I don't ...
- physics ( please help me) - A brick with a mass of 0.400kg is pressed against a ...
- Calculus I - Suppose that f and g are two functions both continuous on the ...