+260 The functions g and h such that
g(x)=2x+5 h(x)=ax+b
where a and b are constants.
h(3)=26 and g^-1(21)=h(1)
Find the value of a and the value of b.
+128408 g(x) = 2x + 5
h(x) = ax + b
If h (3) = 26 we have that 26 =a(3) + b ⇒ 3a + b = 26 (1)
And g-1 (x) is [ x - 5] / 2
So g-1(21) is [ 21 - 5] /2 = 16 /2 = 8
So g-1(21) = 8 = h(1) which implies that
8 = a(1) + b ⇒ a + b = 8 (2)
So...we have the system
3a + b = 26
a + b = 8 subtract the second equation from the first
2a = 18
a = 9
And a + b = 8 so 9 + b = 8 ⇒ b = -1
So the function is
y = 9x - 1
And a = 9 and b = -1
