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f(x) = 34
5x + 4 = 34
5x = 30
x = 6
f⁻¹(34) = 6

f^-1(x)=(x-4)/5
f^-1(34)= (34-4)/5=30/5=6

Let y = f (x) = 5x + 4 and g (y) = x
g is inverse of f

y = 5x + 4
5x = y - 4
x = y/5 - 4/5
g(y) = y/5 - 4/5
g (x) = x/5 - 4/5
g (34) = 34/5 - 4/5 = 30/5 = 6

Option C

The inverse function is basically saying, "what value of x in the original function would give a result of 34"?

So set it to 34:
5x + 4 = 34
5x = 30
x = 30/5
x = 6

So a value of x=6 will result in f(6) = 34.

Therefore f⁻¹(34) = 6

Answer:
c. 6