Determine whether the function has an inverse function. $$ g(x)=\frac{x+1}{8} $$ Yes, $$ g $$ does have an inverse. No, $$ g $$ does not have an inverse. If it does, then find the inverse function. (If an answer does not exist, enter DNE.) $$ g^{-1}(x)= $$

Question

UpStudy AI · Accepted Answer

1. Start with the equation for $$ g(x) $$:
   $$
   y = \frac{x+1}{8}
   $$

2. Multiply both sides by 8 to eliminate the denominator:
   $$
   8y = x+1
   $$

3. Solve for $$ x $$ by subtracting 1 from both sides:
   $$
   x = 8y - 1
   $$

4. To find the inverse function, swap $$ x $$ and $$ y $$ (since the inverse function $$ g^{-1}(x) $$ satisfies $$ y = g^{-1}(x) $$):
   $$
   g^{-1}(x) = 8x - 1
   $$

Yes, $$ g $$ does have an inverse and it is:
$$
g^{-1}(x) = 8x - 1
$$
$$ g^{-1}(x) = 8x - 1 $$

Determine whether the function has an inverse function. \[ g(x)=\frac{x+1}{8} \] Yes, \( g \) does have an inverse. No, \( g \) does not have an inverse. If it does, then find the inverse function. (If an answer does not exist, enter DNE.) \( g^{-1}(x)= \)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions