Answer and Explanation :
We have to find the inverse of the functions below :
1) \(f(x)=2x-3\)
Let f(x)=y
\(y=2x-3\)
Replace the value of x and y,
\(x=2y-3\)
Now we find y,
\(x+3=2y\)
\(y=\frac{x+3}{2}\)
The inverse of the function is \(f^{-1}(x)=\frac{x+3}{2}\)
2) \(f(x)=4x+10\)
Let f(x)=y
\(y=4x+10\)
Replace the value of x and y,
\(x=4y+10\)
Now we find y,
\(x-10=4y\)
\(y=\frac{x-10}{4}\)
The inverse of the function is \(f^{-1}(x)=\frac{x-10}{4}\)
3) \(f(x)=x^4+7\) for x≥0
Let f(x)=y
\(y=x^4+7\)
Replace the value of x and y,
\(x=y^4+7\)
Now we find y,
\(x-7=y^4\)
\(y=(x-7)^{\frac{1}{4}}\)
The inverse of the function is \(g(x)=(x-7)^{\frac{1}{4}}\)
