Given the function f(x)=-1+(7)/(6)x^(2), find the value of f((1)/(7)) in simplest form. Answer:

Given function substitution: We are given the function f(x) = -1 + (7/6)x^2 and we need to find the value of f((1/7)). To do this, we will substitute x with (1/7) in the function.Calculate square: Substitute x = (1/7) into the function f(x) = -1 + (7/6)x^2. f((1/7)) = -1 + (7/6)(1/7)^2Substitute square value: Calculate the square of (1/7). (1/7)^2 = (1^2)/(7^2) = 1/49Multiply fractions: Substitute the value of (1/7)^2 back into the function. f((1/7)) = -1 + (7/6)(1/49)Add to -1: Multiply (7/6) by (1/49). (7/6) * (1/49) = 7/(6*49) = 7/294Find common denominator: Add the result to -1. f((1/7)) = -1 + 7/294Combine fractions: Find a common denominator to combine the terms. The common denominator is 294. -1 can be written as -294/294. f((1/7)) = -294/294 + 7/294Perform addition: Combine the fractions. f((1/7)) = (-294 + 7)/294Write final answer: Perform the addition in the numerator. -294 + 7 = -287Write the final answer. f((1/7)) = -287/294

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Given the function
f(x)=-1+(7)/(6)x^(2), find the value of
f((1)/(7)) in simplest form.
Answer:

Given the function $f(x)=-1+\frac{7}{6} x^{2}$ , find the value of $f\left(\frac{1}{7}\right)$ in simplest form. $\newline$ Answer:

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Algebra 2

Find the vertex of the transformed function

Full solution

Q. Given the function

f(x)=-1+\frac{7}{6} x^{2}

, find the value of

f\left(\frac{1}{7}\right)

in simplest form.

\newline

Answer:

Given function substitution: We are given the function $f(x) = -1 + \frac{7}{6}x^2$ and we need to find the value of $f\left(\frac{1}{7}\right)$ . To do this, we will substitute $x$ with $\frac{1}{7}$ in the function.
Calculate square: Substitute $x = \frac{1}{7}$ into the function $f(x) = -1 + \frac{7}{6}x^2$ . $f\left(\frac{1}{7}\right) = -1 + \frac{7}{6}\left(\frac{1}{7}\right)^2$
Substitute square value: Calculate the square of $(\frac{1}{7})$ . $(\frac{1}{7})^2 = (\frac{1^2}{7^2}) = \frac{1}{49}$
Multiply fractions: Substitute the value of $(\frac{1}{7})^2$ back into the function. $\newline$ $f(\frac{1}{7}) = -1 + (\frac{7}{6})(\frac{1}{49})$
Add to $-1$ : Multiply $\frac{7}{6}$ by $\frac{1}{49}$ . $\newline$ $\frac{7}{6} \times \frac{1}{49} = \frac{7}{6\times49} = \frac{7}{294}$
Find common denominator: Add the result to $-1$ . $\newline$ $f\left(\frac{1}{7}\right) = -1 + \frac{7}{294}$
Combine fractions: Find a common denominator to combine the terms. $\newline$ The common denominator is $294$ . $\newline$ $-1$ can be written as $-294/294$ . $\newline$ $f\left(\frac{1}{7}\right) = -\frac{294}{294} + \frac{7}{294}$
Perform addition: Combine the fractions. $f\left(\frac{1}{7}\right) = \frac{-294 + 7}{294}$
Write final answer: Perform the addition in the numerator. $\newline$ $-294 + 7 = -287$
Write final answer: Perform the addition in the numerator. $\newline$ $-294 + 7 = -287$ Write the final answer. $\newline$ $f\left(\frac{1}{7}\right) = \frac{-287}{294}$