Question

Let $f(x)=1 / x$ and $$g(x)=\left\{\begin{array}{ll}{\frac{1}{x}} & {\text { if } x > 0} \\ {1+\frac{1}{x}} & {\text { if } x < 0}\end{array}\right.$$ Show that $f^{\prime}(x)=g^{\prime}(x)$ for all $x$ in their domains. Can we conclude from Corollary 7 that $f-g$ is constant?

          Let $f(x)=1 / x$ and 
$$g(x)=\left\{\begin{array}{ll}{\frac{1}{x}} & {\text { if } x > 0} \\ {1+\frac{1}{x}} & {\text { if } x < 0}\end{array}\right.$$ 
Show that $f^{\prime}(x)=g^{\prime}(x)$ for all $x$ in their domains. Can we
conclude from Corollary 7 that $f-g$ is constant?

Added by David F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/27/2022

Step 1

Step 1:** Given functions: \[ f(x) = \frac{1}{x} \] \[ g(x) = \begin{cases} \frac{1}{x} & \text{if } x > 0 \\ 1 + \frac{1}{x} & \text{if } x < 0 \end{cases} \] ** Show more…

Show all steps

Thanks for your feedback!

Let $f(x)=1 / x$ and $$g(x)=\left\{\begin{array}{ll}{\frac{1}{x}} & {\text { if } x > 0} \\ {1+\frac{1}{x}} & {\text { if } x < 0}\end{array}\right.$$ Show that $f^{\prime}(x)=g^{\prime}(x)$ for all $x$ in their domains. Can we conclude from Corollary 7 that $f-g$ is constant?