document.write( "Question 1194864: Let 𝑓 be the function with correspondence rule 𝑓(𝑥) = 3𝑥^2 + 5𝑥 − 3 with 𝑥 ∈ [0; +∞[, determine the inverse function 𝑓^−1 and its domain. \n" ); document.write( "

Algebra.Com's Answer #827143 by shlomitg(8) $\"\"$ $\"About$

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𝑓^−1(x)=1/(3𝑥^2 + 5𝑥 − 3) where 𝑥 ∈ [0; +∞] excluding xi which would lead to 1/0
\n" ); document.write( "Solving 3𝑥^2 + 5𝑥 − 3 = 0 we get x1=[-5-sqrt(61)]/6 x2=[-5+sqrt(61)]/6
\n" ); document.write( "x1=[-5-sqrt(61)]/6 <0 therefore not in the domain of the function\r
\n" ); document.write( "\n" ); document.write( " x2=[-5+sqrt(61)]/6>0 therefore in the domain of f(x), but not in the domain of 𝑓^−1(x) since it would lead to a value of 1/0 \r
\n" ); document.write( "\n" ); document.write( "so the domain of 𝑓^−1(x) is 𝑥 ∈ [0; +∞] excluding [-5+sqrt(61)]/6]=0.468 \n" ); document.write( "

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