Write as a Function of T T^-1(a)=11a-2

$T^{- 1} (a) = 11 a - 2$

Step 1

Simplify $T^{- 1} a$ .

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{T} a = 11 a - 2$

Combine $\frac{1}{T}$ and $a$ .

$\frac{a}{T} = 11 a - 2$

Step 2

Subtract $11 a$ from both sides of the equation.

$\frac{a}{T} - 11 a = - 2$

Step 3

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$T, 1, 1$

The LCM of one and any expression is the expression.

$T$

Step 4

Multiply each term in $\frac{a}{T} - 11 a = - 2$ by $T$ to eliminate the fractions.

Multiply each term in $\frac{a}{T} - 11 a = - 2$ by $T$ .

$\frac{a}{T} T - 11 a T = - 2 T$

Simplify the left side.

Cancel the common factor of $T$ .

Cancel the common factor.

$\frac{a}{T} T - 11 a T = - 2 T$

Rewrite the expression.

$a - 11 a T = - 2 T$

Step 5

Solve the equation.

Factor $a$ out of $a - 11 a T$ .

Raise $a$ to the power of $1$ .

$a - 11 a T = - 2 T$

Factor $a$ out of $a^{1}$ .

$a \cdot 1 - 11 a T = - 2 T$

Factor $a$ out of $- 11 a T$ .

$a \cdot 1 + a (- 11 T) = - 2 T$

Factor $a$ out of $a \cdot 1 + a (- 11 T)$ .

$a (1 - 11 T) = - 2 T$

Divide each term in $a (1 - 11 T) = - 2 T$ by $1 - 11 T$ and simplify.

Divide each term in $a (1 - 11 T) = - 2 T$ by $1 - 11 T$ .

$\frac{a (1 - 11 T)}{1 - 11 T} = \frac{- 2 T}{1 - 11 T}$

Simplify the left side.

Cancel the common factor of $1 - 11 T$ .

Cancel the common factor.

$\frac{a (1 - 11 T)}{1 - 11 T} = \frac{- 2 T}{1 - 11 T}$

Divide $a$ by $1$ .

$a = \frac{- 2 T}{1 - 11 T}$

Simplify the right side.

Move the negative in front of the fraction.

$a = - \frac{2 T}{1 - 11 T}$

Step 6

To rewrite as a function of $T$ , write the equation so that $a$ is by itself on one side of the equal sign and an expression involving only $T$ is on the other side.

$f (T) = - \frac{2 T}{1 - 11 T}$

Write as a Function of T T^-1(a)=11a-2

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