algebra problem?

Question

Suppose that (gºf)(x) = 3x+7. Find g(x) if f(x) = 4- 11x. Find f(x) of g(x) =4 -11x. I know that the answers are g(x) = (-3/11)x+ (89/11) and f(x)=(-3/11)x - (3/11) but I don't know how to solve this problem or what to look up on the internet to find information.

Answer 1

Hi,

If (g◦f)(x) = 3x + 7 and f(x) = 4 - 11x. Suppose g(x) = b + ax, where a and b are rational numbers.

Then (g◦f)(x) = b + a(4 - 11x) = b + 4a - 11ax. Then the x term, -11ax = 3x from (g◦f)(x) = 3x + 7.
Solving -11ax = 3x, gives a = -3/11.

The constant above is b + 4a and that equals 7 in (g◦f)(x).
So b + 4a = 7. Plugging in -3/11 for a gives:
b + 4(-3/11) = 7
b - 12/11 = 7
b = 7 + 12/11
b = 77/11 + 12/11
b = 89/11

So g(x) is -3/11x + 89/11.

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If (g◦f)(x) = 3x + 7 and g(x) = 4 - 11x. Suppose f(x) = cx + d, where c and d are rational numbers.

Then (g◦f)(x) = 4 - 11(cx + d) = 4 - 11cx - 11d. Then the x term, -11cx = 3x from (g◦f)(x) = 3x + 7.
Solving -11cx = 3x, gives c = -3/11.

The constant above is 4 - 11d and that equals 7 in (g◦f)(x).
So 4 - 11d = 7.
- 11d = 3
d = -3/11

So f(x) = -3/11x - 3/11



I hope that helps!! :-)


Happy 4th!!!

Answer 2

you want g(f(x) = 3x+7, and you have f(x) = 4-11x. so g(4-11x) = 3x+7. g has to turn -11x into 3x, which needs multiplication by -3/11. -3/11(4-11x) = 3x - 12/11. we need to add enough to turn -12/11 into 7, which is 77/11, so we add 89/11. that makes g(x) = -3/11x + 89/11.

approach the other problem the same way, 1st the multiplication, then the addition.

Answer 3

hi pal this an trouble-free question consistent with linear equations you need to use transposition technique in this technique whilst a term is transfered from one area to different its sign turns into opposite answer: x+4-7x=22 =4-7x=22-x (right here x comes from the left area its sign ameliorations) =4=22-x+7x(right here 7x comes from the left area its sign ameliorations) =4-22=6x(comparable) =-18=6x x=-18/6 =-3 Bye Bye!!!!!!!!!!!!!!!!!!!!!!