All SAT Math Resources
Example Questions
Example Question #1081 : Algebra
If and , what is ?
Whenever there is a function, all you need to do is plug in the value into the function. Since this is multi-function, whichever answer we get for the inside function, we plug it into the outer function.
;
Example Question #1081 : Algebra
If and , then what is ?
Whenever there is a function, all you need to do is plug in the value into the function. Since this is multi-function, whichever answer we get for the inside function, we plug it into the outer function.
and
Example Question #1082 : Algebra
If , then what value of will make true?
We know and . Just set them equal to each other.
Subtract on both sides.
Divide on both sides.
Example Question #1082 : Algebra
If , then what value of will make true?
We know and . Just set them equal to each other.
Subtract on both sides.
Take square root on both sides and account for also negative answers.
Example Question #1083 : Algebra
If then what value of will make true?
We know that and . Just set them equal to each other.
Remember to account for negative values.
Subtract on both sides.
Subtract on both sides.
Example Question #1083 : Algebra
If and then what value of will make true?
We know so we need to apply substitutions to solve for .
Subtract on both sides.
Take square root on both sides and account for negative values.
Example Question #111 : How To Find F(X)
If , then what value of will make
We know so let's make the substitution.
This is a quadratic so subtract on both sides.
Factor.
Solve individually.
Example Question #1085 : Algebra
Define .
How can be defined so that ?
By definition,
,
so
If
,
it follows that
,
and, substituting,
Solving for by isolating this expression:
.
Example Question #1086 : Algebra
Define .
How can be defined so that ?
By definition,
,
so
If
,
it follows that
,
and, substituting,
Solving for by isolating this expression:
Taking the square root of both sides:
Either , which is not among the given choices, or , which is.
Example Question #1087 : Algebra
Define .
How can be defined so that ?
By definition,
,
so
If
,
it follows that
,
and, substituting,
Solving for by isolating this expression:
Applying the Power of a Product Rule: