Activity - Given: $$ f(x)=-x+2, \quad g(x)=2 x^{2}-1, \quad h(x)=\frac{1}{x} $$ Determine: $$ \begin{array}{lllll} ext { a) } f(-1) & ext { b) } g(a) & ext { c) } h\left(\frac{1}{2} ight) & ext { d) } f(a+2) & ext { e) } f(a)+g(a)\end{array} \quad $$ f) $$ h\left(\frac{1}{x} ight) $$ $$ \begin{array}{llll} ext { E) } g(-2)+h(2)-f(3) & ext { h] } f(x) imes g(0) & ext { i) } f[g(0)] & ext { ] } g[h(-2)]\end{array} $$

Question

Activity - Given: $$ f(x)=-x+2, \quad g(x)=2 x^{2}-1, \quad h(x)=\frac{1}{x} $$ Determine: $$ \begin{array}{lllll}	ext { a) } f(-1) & 	ext { b) } g(a) & 	ext { c) } h\left(\frac{1}{2}ight) & 	ext { d) } f(a+2) & 	ext { e) } f(a)+g(a)\end{array} \quad $$ f) $$ h\left(\frac{1}{x}ight) $$ $$ \begin{array}{llll}	ext { E) } g(-2)+h(2)-f(3) & 	ext { h] } f(x) 	imes g(0) & 	ext { i) } f[g(0)] & 	ext { ] } g[h(-2)]\end{array} $$

UpStudy AI · Accepted Answer

We are given the functions

f(x) = –x + 2  
  g(x) = 2x² – 1  
  h(x) = 1/x

Below are the steps to compute each part.

──────────────────────────────
a) f(–1)

f(–1) = –(–1) + 2  
     = 1 + 2  
     = 3

──────────────────────────────
b) g(a)

Replace x by a:

g(a) = 2(a)² – 1  
     = 2a² – 1

──────────────────────────────
c) h(½)

h(½) = 1/(½)  
     = 2

──────────────────────────────
d) f(a + 2)

f(a + 2) = –(a + 2) + 2  
     = –a – 2 + 2  
     = –a

──────────────────────────────
e) f(a) + g(a)

First, find f(a) and g(a) separately:

f(a) = –a + 2  
 g(a) = 2a² – 1

Now add:

f(a) + g(a) = (–a + 2) + (2a² – 1)  
         = 2a² – a + 1

──────────────────────────────
f) h(1/x)

Replace x by 1/x in h(x):

h(1/x) = 1/(1/x)  
     = x             (provided x ≠ 0)

──────────────────────────────
Next, we have additional expressions:

──────────────────────────────
E) g(–2) + h(2) – f(3)

First, compute each term:

• g(–2) = 2(–2)² – 1 = 2(4) – 1 = 8 – 1 = 7  
 • h(2) = 1/2  
 • f(3) = –3 + 2 = –1

Now, combine:

g(–2) + h(2) – f(3) = 7 + (1/2) – (–1)  
               = 7 + 1/2 + 1  
               = 8 + 1/2  
               = 17/2

──────────────────────────────
h] f(x) × g(0)

First, compute g(0):

g(0) = 2·0² – 1 = –1

Now, multiply by f(x):

f(x) × g(0) = f(x) × (–1) = –f(x)

Since f(x) = –x + 2, we have:

–f(x) = –(–x + 2) = x – 2

──────────────────────────────
i) f[g(0)]

Since we already found g(0) = –1, then

f[g(0)] = f(–1) = 3        (as computed in part a)

──────────────────────────────
] g[h(–2)]

First, find h(–2):

h(–2) = 1/(–2) = –½

Now, compute g(–½):

g(–½) = 2(–½)² – 1 = 2(¼) – 1 = ½ – 1 = –½

──────────────────────────────
Final Answers Summary:

a) f(–1) = 3

b) g(a) = 2a² – 1

c) h(1/2) = 2

d) f(a + 2) = –a

e) f(a) + g(a) = 2a² – a + 1

f) h(1/x) = x         (x ≠ 0)

E) g(–2) + h(2) – f(3) = 17/2

h] f(x) × g(0) = x – 2

i) f[g(0)] = 3

] g[h(–2)] = –½

Any answer written in equivalent form is correct.
a) $$ f(-1) = 3 $$ b) $$ g(a) = 2a^2 - 1 $$ c) $$ h\left(\frac{1}{2}ight) = 2 $$ d) $$ f(a + 2) = -a $$ e) $$ f(a) + g(a) = 2a^2 - a + 1 $$ f) $$ h\left(\frac{1}{x}ight) = x $$ (for $$ x 
eq 0 $$) E) $$ g(-2) + h(2) - f(3) = \frac{17}{2} $$ h) $$ f(x) 	imes g(0) = x - 2 $$ i) $$ f[g(0)] = 3 $$ ] $$ g[h(-2)] = -\frac{1}{2} $$

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