given the function ( f(x)=x^{3}-5 ), complete parts a through c.\n(a) find an equation for ( f^{-1}(x)…

given the function ( f(x)=x^{3}-5 ), complete parts a through c.\n(a) find an equation for ( f^{-1}(x) ).\n(b) graph ( f ) and ( f^{-1} ) in the same rectangular coordinate system.\n(c) use interval notation to give the domain and the range of ( f ) and ( f^{-1} ).\n(a) find ( f^{-1}(x) ).\n( f^{-1}(x)=square )\n(type an exact answer, using radicals as needed.)

given the function ( f(x)=x^{3}-5 ), complete parts a through c.\n(a) find an equation for ( f^{-1}(x) ).\n(b) graph ( f ) and ( f^{-1} ) in the same rectangular coordinate system.\n(c) use interval notation to give the domain and the range of ( f ) and ( f^{-1} ).\n(a) find ( f^{-1}(x) ).\n( f^{-1}(x)=square )\n(type an exact answer, using radicals as needed.)

Answer

Explanation:

Step1: Replace ( f(x) ) with ( y )

Let ( y = x^{3}-5 )

Step2: Swap ( x ) and ( y )

We get ( x = y^{3}-5 )

Step3: Solve for ( y )

Add ( 5 ) to both sides: ( x + 5=y^{3} ) Take the cube - root of both sides: ( y=\sqrt[3]{x + 5} )

Answer:

( f^{-1}(x)=\sqrt[3]{x + 5} )