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August 2, 2014

August 2, 2014

Posted by **CHLOE** on Wednesday, December 19, 2012 at 6:13am.

Q)

Two functions f and g are defined by

f:x (arrow) x^2 + 3

g:x (arrow) 2x+1

Find

a) the function fg

b) solve the equation f(x)=12g^-1(x)

I need to show my working out, please help someone

- MATHS -
**Steve**, Wednesday, December 19, 2012 at 11:02amby fg I assume you mean f*g

f*g = (x^2+3)*(2x+1) = 2x^3 + x^2 + 6x + 3

g=2x+1, so g^-1 = (x-1)/2

so, if f = 12 g^-1,

x^2+3 = 12 * (x-1)/2

x^2+3 = 6x-6

x^2 - 6x + 9 = 0

(x-3)^2 = 0

x = 3

- MATHS -
**CHLOE**, Wednesday, December 19, 2012 at 2:08pmThank you steve

It says i need to find f(g), i got a different result for some reason help please!

And also in the second part, how did you get g^-1 = (x-1)/2

Thank you steve x

- MATHS -
**Steve**, Wednesday, December 19, 2012 at 2:36pmThat's because fg is ambiguous. I did f(x) * g(x).

f◦g = f(g) = g^2+3 = (2x+1)^2+3

= 4x^2 + 4x + 4

to get g^-1, just solve for x

g = 2x+1

g-1 = 2x

x = (g-1)/2

then switch variables, and g^-1 = (x-1)/2

- MATHS -
**CHLOE**, Wednesday, December 19, 2012 at 3:51pmIs there any reason why f(g)=g^2+3

why do we replace the x with g?

Sorry steve im trying my hardest to understand this

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