Function given, find values of x if...

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In summary, the general process for finding values of x given a function is to first identify the given function and any restrictions or conditions mentioned. Then, use algebraic manipulation and substitution to isolate the variable x and solve for its value. This can also be done using a calculator, but it is important to ensure the correct mode is set and to double check the answer. Multiple solutions for x may exist if the function intersects the x-axis more than once or has multiple terms with x raised to different powers. Special cases to be aware of include functions with rational expressions, logarithms, or trigonometric functions. The quadratic formula can only be used for quadratic functions, and other methods may be needed for finding values of x for other types of functions
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Bia1
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f(x)=3\sqrt{x+4} & x\ge-4;y\ge0

then if f(x)\ge4 find the values of x

Do I then ignore x\ge-4;y\ge0 and replace f(x) with 4 ?

How would I go about solving this?
 
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Hint: start with \(\displaystyle x+4=\dfrac{16}{9}\)

*Note: for LaTeX to render correctly here enclose your code in [math]...[/math] tags.
You may also use $$...$$. Use $...$ for inline code.
 
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FAQ: Function given, find values of x if...

What is the general process for finding values of x given a function?

The general process for finding values of x given a function is to first identify the given function and any restrictions or conditions mentioned. Then, use algebraic manipulation and substitution to isolate the variable x and solve for its value.

Can I use a calculator to find values of x for a given function?

Yes, you can use a calculator to find values of x for a given function. However, it is important to make sure your calculator is set to the correct mode (e.g. radians or degrees) and to double check your answer by plugging it back into the original function.

How do I know if there are multiple solutions for x in a given function?

If the given function is an equation, you can determine if there are multiple solutions for x by graphing the function and looking for any points where the graph intersects the x-axis more than once. Alternatively, you can also check if the function has multiple terms with the variable x raised to different powers, as this can indicate multiple solutions.

Are there any special cases I should be aware of when finding values of x for a given function?

Yes, there are some special cases to be aware of when finding values of x for a given function. These can include functions with rational expressions, logarithms, or trigonometric functions, which may require additional steps or restrictions in order to solve for x.

Can I use the quadratic formula to find values of x for any given function?

No, the quadratic formula can only be used to find values of x for quadratic functions (functions with the form ax^2 + bx + c). For other types of functions, you may need to use different methods such as factoring, completing the square, or graphing to find values of x.

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