what is the inverse of the function $f(x) = 2x - 10$?\n$\\circ$ $h(x) = 2x - 5$\n$\\circ$ $h(x) = 2x +…

what is the inverse of the function $f(x) = 2x - 10$?\n$\\circ$ $h(x) = 2x - 5$\n$\\circ$ $h(x) = 2x + 5$\n$\\circ$ $h(x) = \\frac{1}{2}x - 5$\n$\\circ$ $h(x) = \\frac{1}{2}x + 5$
Answer
Explanation:
Step1: Replace ( f(x) ) with ( y )
We start with the function ( f(x) = 2x - 10 ). Replace ( f(x) ) with ( y ), so we have ( y = 2x - 10 ).
Step2: Swap ( x ) and ( y )
To find the inverse, we swap the roles of ( x ) and ( y ). This gives us ( x = 2y - 10 ).
Step3: Solve for ( y )
First, add 10 to both sides of the equation: ( x + 10 = 2y ). Then, divide both sides by 2: ( y=\frac{1}{2}x + 5 ). So the inverse function ( h(x)=\frac{1}{2}x + 5 ).
Answer:
( h(x)=\frac{1}{2}x + 5 ) (the fourth option: ( h(x)=\frac{1}{2}x + 5 ))