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If possible, find all values of a such that there are no x- intercepts for f(x)=2|x+1|+a.

Sagot :

XKelvinidn

Answer:

[tex]\displaystyle a > 0[/tex]

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = 2|x+1| + a[/tex]

And we want to find all values of a such that the are no x-intercepts.

Recall that an x-intercept is when the graph crosses the x-axis. So, let y = 0:

[tex]\displaystyle \left(0\right) = 2|x+1| + a[/tex]

Isolate the absolute value:

[tex]\displaystyle - \frac{1}{2} a = |x+1|[/tex]

Absolute value only outputs zero or positive values. So, in order for the function to have no x-intercepts, the left-hand side must be negative. That is:

[tex]\displaystyle -\frac{1}{2} a < 0[/tex]

Solve for a:

[tex]\displaystyle a > 0[/tex]

In conclusion, the value of a for which the given function has no solution is all real numbers greater than zero.

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