To find the inverse of a one-to-one function, do the following: 1. If the function is written in function notation, replace f(x)f(x) with yy. 2. Swap any xx in the function with yy, and vice versa, i.e., y=x+2y=x+2 becomes x=y+2x=y+2. 3. Solve for yy, then replac...
Algebra Examples Popular Problems Algebra Solve for x sin(arcsin(x))=1 sin(arcsin(x))=1sin(arcsin(x))=1 Take theinversesineof both sides of theequationto extractarcsin(x)arcsin(x)from inside thesine. arcsin(x)=arcsin(1)arcsin(x)=arcsin(1) ...
Precalculus Examples cot(x)+1=0cot(x)+1=0 Subtract11from both sides of theequation. cot(x)=−1cot(x)=-1 Take theinversecotangentof both sides of theequationto extractxxfrom inside thecotangent. x=arccot(−1)x=arccot(-1)
Trigonometry Examples tan(x)=0.8949tan(x)=0.8949 Take theinversetangentof both sides of theequationto extractxxfrom inside thetangent. x=arctan(0.8949)x=arctan(0.8949) Simplify the right side. Tap for more steps... arctan(0.8949).
Take theinversetangentof both sides of theequationto extractθθfrom inside thetangent. θ=arctan(1)θ=arctan(1) Simplify the right side. Tap for more steps... The exact value ofarctan(1)is45. θ=45 θ=45θ=45 Thetangentfunctionis positive in the first and thirdquadrants. To find ...
Take theinversesineof both sides of theequationto extractθθfrom inside thesine. θ=arcsin(0)θ=arcsin(0) Simplify the right side. Tap for more steps... The exact value ofarcsin(0)is0. θ=0 θ=0θ=0 Thesinefunctionis positive in the first andsecondquadrants. To find thesecondsolutio...
Precalculus Examples tan2(x)=4tan2(x)=4 Take the specifiedrootof both sides of theequationtoeliminatetheexponenton the left side. tan(x)=±√4tan(x)=±4 Simplify±√4±4. Tap for more steps... Rewrite4as22. tan(x)=±22
Factortan(x)tan(x)out of2sin(x)tan(x)+tan(x)2sin(x)tan(x)+tan(x). Tap for more steps... tan(x)out of2sin(x)tan(x). tan(x)(2sin(x))+tan(x)=0 Raisetan(x)to theof1. tan(x)(2sin(x))+tan(x)=0 tan(x)out oftan1(x). ...
Precalculus Examples cos(x)=√cos(x)=32 Multiplyeachtermby afactorof11that will equate all thedenominators. In this case, alltermsneed adenominatorof22. cos(x)⋅22=√32cos(x)2232 Multiply expression factor least common denominator
finding the inverse To find the inverse of a one-to-one function, do the following: 1. If the function is written in function notation, replace f(x)f(x) with yy. 2. Swap any xx in the function with yy, and vice versa, i.e., y=x+2y=x+2 becomes x=y+2x=y+2. 3. Solve ...