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3 years ago

Determine the equation of the inverse of y = e x + 3 - 4

Mathematics

1 answer:

pochemuha3 years ago

4 0

ANSWER

${f}^{ - 1} (x) = ln(x + 4) - 3$

EXPLANATION

We want to find the equation of the inverse of

$y = {e}^{x + 3} - 4$

First, we need to interchange x and y.

$x= {e}^{y + 3} - 4$

Solve for y,

$x + 4={e}^{y + 3}$

Take the natural logarithm of both sides,

$ln(x + 4)= ln{e}^{y + 3}$

Simplify

$ln(x + 4)= y + 3$

$ln(x + 4) - 3= y$

Hence the inverse function is,

${f}^{ - 1} (x) = ln(x + 4) - 3$

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pantera1 [17]

Answer:

y = 8 is the equation of tangent.

Step-by-step explanation:

The equation of the tangent to the circle at (-6,8) is of the form:

y = mx + c

where m is the slope of the tangent and c is the y-intercept.

The point (-6,8) lies on the circle and the tangent line as well.

Hence (-6,8) satisfies the line equation:

8 = m(-6) + c ⇒ c-6m = 8 -------------1

We know that slope of two perpendicular lines are related as:

$m_{1}\times m_{2}=-1$

At any point on the circle, the normal line at a point is always perpendicular to the tangent line at that point.

Hence :

$m_{normal} \times m_{tangent}=-1$

We can find the slope of the normal at point (-6,8) as it passes through the centre of the circle (-6,4) by using the two-points formula for slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{8-4}{-6+6}$

= ∞

Slope of the normal is infinity and hence slope of tangent is -1/∞ = 0

Hence m=0

Putting m=0 in equation 1 we get:

c = 8

The equation of tangent line at (-6,8) is:

y = 8

6 0

3 years ago

Find the equivalent expression of 3+2(2p+4t)

NISA [10]

Remember to follow PEMDAS, and to only combine terms with like variables.

First, distribute the 2 to all terms within the parenthesis:

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3 + 4p + 8t, or (D), is your answer choice, for it cannot be simplified anymore.

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4 years ago

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and this would have led to the same result.

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Step-by-step explanation:

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