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Question 803502: I need to find the domain of the following function algebraically. f(x)=4x-7
Answer by cabdi809(1)   (Show Source):
You can put this solution on YOUR website!
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
All real numbers
i did it by inverse
f(x)=4x−7
To find the inverse of the function, interchange the variables and solve for y.
x=4y−7
Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
4y−7=x
Since −7 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 7 to both sides.
4y=7+x
Move all terms not containing y to the right-hand side of the equation.
4y=x+7
Divide each term in the equation by 4.
4y4=14x+74
y=14x+74
Replace the y with f−1(x) to show the final answer.
f−1(x)=14x+74
Find the composition of f(x)=4x−7 and its inverse f−1(x)=x4+74 to verify it is the inverse of f(x)=4x−7. If f(f−1(x))=x, then f−1(x)=x4+74 is the inverse of f(x).
Verify f(f−1(x))=x
Find the composition f(f−1(x)).
More Detail
f(14x+74)=x
Since f(f−1(x))=x,f−1(x)=x4+74 is the inverse of f(x)=4x−7.
f−1(x)=14x+74
I hope that helped
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