The correct option is Option D: the value of g(1) is 4.
What is the Inverse function?
An inverse function is a function which reverses the function direction for which the range of the function becomes the domain and the domain of the function becomes the range of the inverse function.
If y = f(x) is the given function then x = f⁻¹(y) is the inverse function.
Here, given in the question the value of x and the value of f(x).
for which f(-1)= -3
f(1)= -1
f(4)= 1
f(6)= 4
f(7)= 6
So let the value of f(x) is y
we can write y=f(x)
applying inverse on both side
⇒f⁻¹(y)= f⁻¹(f(x))
⇒f⁻¹(y)= x
⇒ x= f⁻¹(y)
given that the inverse of f(x) is g(x)
so now the equation will be
⇒ x= f⁻¹(y)=g)y)
⇒ x= g(y)
according to the above function at the value of y, the inverse of the function will be g(y)= f⁻¹(y)
so from the table it is clear that at the value of x=4, f(x)=y=1.
So at y=1, 1=f(4)
so applying inverse on both side
⇒ f⁻¹(1)= f⁻¹(f(4))
⇒ f⁻¹(1)= 4
⇒g(1)= 4
Therefore the value of the g(1)= 4.
Learn more about inverse function
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