Suggested languages for you:

Americas

Europe

Q 95.

Expert-verifiedFound in: Page 544

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**Determining Identities Graphically**

**Graph $f$ and $g$ in the same viewing rectangle. Do the graphs suggest that the equation $\mathit{f}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}\mathit{g}\mathbf{\left(}\mathit{x}\mathbf{\right)}$ is an identity? Prove your answer**

**$\mathit{f}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}\mathit{c}\mathit{o}{\mathit{s}}^{\mathbf{2}}\mathit{x}\mathbf{-}\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{2}}\mathit{x}\mathbf{,}\mathbf{\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}}\mathit{g}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}\mathbf{1}\mathbf{-}\mathbf{2}\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{2}}\mathit{x}$**

The expression $f\left(x\right)=g\left(x\right)$ is an identity.

Two functions as-

$\begin{array}{l}f\left(x\right)={\mathrm{cos}}^{2}x-{\mathrm{sin}}^{2}x\\ \text{\hspace{0.33em}}g\left(x\right)=1-2{\mathrm{sin}}^{2}x\end{array}$

Create distinct graphs for both functions on the same graph. Both functions are equivalent if both graphs coincide with one other. As a result, combining them into a single equation yields an identity.

Now, draw graphs of both functions:

Since both graphs coincide each other. Therefore $f\left(x\right)=g\left(x\right)$ is an identity

94% of StudySmarter users get better grades.

Sign up for free