Answer
$g(\frac{1}{2})\approx 0.192$;
$g(\sqrt2) \approx 0.070$;
$g(-3.5)\approx 15.588$;
$g(\frac{1}{4}) \approx 1.552$
Work Step by Step
Evaluate the function for the given values of $x$ by substituting each $x$ into $g(x)$ then using a calculator to find the exact value.
When x=$\frac{1}{2}$:
$g(x) = \left(\dfrac{1}{3}\right)^{x+1}
\\g(\frac{1}{2})=\left(\dfrac{1}{3}\right)^{\frac{1}{2}+1}
\\g(\frac{1}{2})=\left(\dfrac{1}{3}\right)^{\frac{3}{2}}
\\g(\frac{1}{2})\approx 0.192$
When $x=\sqrt2$:
$g(x) = \left(\dfrac{1}{3}\right)^{x+1}
\\g(\sqrt2) = \left(\dfrac{1}{3}\right)^{\sqrt2+1}
\\g(\sqrt2) \approx 0.070$
When $x=-3.5$:
$g(x)=\left(\dfrac{1}{3}\right)^{x+1}
\\g(-3.5)=\left(\dfrac{1}{3}\right)^{-3.5+1}
\\g(-3.5)=\left(\dfrac{1}{3}\right)^{-2.5}
\\g(-3.5)\approx 15.588$
When $x=-1.4$:
$g(x)=\left(\dfrac{1}{3}\right)^{x+1}
\\g(\frac{1}{4}) = \left(\dfrac{1}{3}\right)^{-1.4+1}
\\g(\frac{1}{4}) = \left(\dfrac{1}{3}\right)^{-0.4}
\\g(\frac{1}{4}) \approx 1.552$
