Answer:
a=6
b=-2
Step-by-step explanation:
You can use the hint provided on the mathswatch question page, I've attached it below
step 1
h(4) = ax+b = (ax4)+b = 4a+b
it is given in the question that h(4)=22, therefore 4a+b=22
step 2
work out the equation for inverse g
g^-1(x) = [tex]\frac{x-2}{3}[/tex]
step 3
input 14 into the equation in place of x to find g^-1(x)
[tex]\frac{x-2}{3} =\frac{14-2}{3} =\frac{12}{3} =4[/tex]
so, g(x)^-1=4
step 4
find h(1):
h(1) = (ax1)+b = a+b
so, h(1)=a+b
step 5
a+b=4 (as it is given in the question that g^-1(14) is equal to h(1))
step 6
Now you have two simultaneous equations:
4a+b=22
a+b=4
then, solve for a:
4a+b=22
- a+b=4
3a=18
a=6
then, input answer for a into either equation (I've gone with the a+b=4 equation):
6+b=4
-6 - 6
b=-2
(p.s i know this is very late but hope it helps someone)
