<span>3t - 2/3=1+t
we need to separate t. subtract t from both sides.
2t - 2/3 = 1
add 2/3 to both sides.
2t = 1+2/3
2t = 3/3 + 2/3
2t = 5/3
divide 2 by both sides.
t = 5/6</span>

5 0

3 years ago

If f(x) = 6x – 4, then f^-1(x)=

guapka [62]

Answer:

$f^{-1}(x)=\frac{x}{6}+\frac{2}{3}$

Step-by-step explanation:

Given function.

$f(x)=6x-4$

To find the inverse function $f^{-1}(x)$

Step 1:

Replace $f(x)$ with $y$ in the function.

$y=6x-4$

Step 2:

Interchange $y$ with $x$ in the equation.

$x=6y-4$

Step 3:

Solve for $y$ .

We have $x=6y-4$

Adding 4 to both sides,

$x+4=6y-4+4$

$x+4=6y$

Dividing each term by 6 to isolate $y$

$\frac{x}{6}+\frac{4}{6}=\frac{6y}{6}$

$\frac{x}{6}+\frac{4}{6}=y$

Simplifying fractions by dividing the numerator and denominator by their GCF.

$\frac{x}{6}+\frac{4\div 2}{6\div 2}=y$

$\frac{x}{6}+\frac{2}{3}=y$

Thus the equation of $y$ is:

$y=\frac{x}{6}+\frac{2}{3}$

Step 4:

Replace $y$ with $f^{-1}(x)$

$f^{-1}(x)=\frac{x}{6}+\frac{2}{3}$ (Answer)

Thus, we have the inverse function

8 0

3 years ago

Two math students were asked to describe the exponential equation: y=230(0.98)^x

nikdorinn [45]

Answer:

See below

Step-by-step explanation:

Its an equation of decay because continuous multiplication by 0.98 decreases the value of the function as x increases. Its gradual slow decay because 0.98 is just below 1. The graph will pass through the point (0,230) ( when x = 0) and is continuous over the range of all real numbers. The graph is not a straight line but slightly curved.

4 0

3 years ago