f(x)= a+tan(bx)

Question

fina a and b

f(0)= 5

f(pi/8)=1/sq root of 3 +5

Answer 1

f(x) = a + tan(bx)
f(0) = 5 ---> 5 = a+tan(0)
a = 0

so f(x) = 5 + tan(bx)
f(π/8) = 1/√3 + 5

1/√3 + 5 = 5 + tan(πb/8)
1/√3 = tan (bπ/8)
We know tan(π/6) = 1/√3
so
bπ/8 = π/6
b = 8/6 = 4/3

f(x) = 5 + tan(4x/3)