Question

Given that $f(x)=2ax+5b$ and $g(x)=ax-4b$
If $g^{-1} (3) = 4$ and $f(1)=1$
Find the values of a and b

Please show working

Answer 1

Answer:

a= 19/8    b=-1/14

Step-by-step explanation:

f(x)=2ax+5b

g(x)=ax-4b

g^{-1} (3) = 4 and f(1)=1

Now

f(1)=2a(1)+5b

2a+5b=1..........\1\

Also

g^{-1} (3) = 4

g(4)=3

g(4)=a(4)-4b

4a-4b=3..........\2\

From \1\ and \2\

    4a+10b=2

(-)  (4a-4b=3)

    14b=-1

       b= -1/14

Now

a=(4b+3)/4

a=19/8

Hope it Helps